Baby has only one wing!

I bought my first chickens ever at the end of March... A Momma hen and 5 chicks. And no, I don't have the faintest idea what breed they are. Needless to say, I'm pretty ignorant about raising chickens, but am so looking forward to fresh eggs and eventually, fresh meat. I joined this forum yesterday and have spent many hours over the past few days looking around and getting answers to questions I didn't even know I had! Like what to feed them and how to build a predator proof coop and truck. HOWEVER... there are a few questions I have that I haven't been able to find answers to.

The chicks were about 4-6 weeks old when I got them so they are about 10-12 weeks old now. I haven't handled them at all yet b/c the hen is a fierce Mother and quite frankly, she intimidates me. I didn't notice anything wrong with any of the chicks for about a week. Then I noticed that the smallest one had only one wing when it tried to flex the wings out. It's got this little stub on the other side... very weird, but other than that, it seems to be in good health. It's actually the cutest of my little flock! So I'm wondering if I should cull this one out or keep it.

Also, how old will the chicks be when Momma finally quits caring for them and starts laying again? The lady who sold me these chicks has been trying to get me to buy a rooster, saying the rooster will get Momma going on production again, but I don't want to buy a rooster 'cause I suspect that the chances are pretty good that at least one of my chicks is a rooster.

As long as the single winged one can get to roosts and you have shelter from predators, I would say it's fine. They don't really NEED wings. There are a number of folks here who have chickens who've been injured and had wings or even LEGS amputated ant they're fine. As long as it has at least 1 leg and seems healthy, let it be!

I think the lady is just trying to get rid of a rooster. Dont give in. Your hen will start laying again when she feels the babies are ok with out her. My one broody hatched in august and 6 wks later was laying again. The other broody hatched in september and stopped. I sold her in febuary and she hadnt started again. I think the breed might influence that. Idk for sure. I would wait to get ANY other chickens untill the chicks were bigger to avoid a new chicken hurting them.